When Peter Santis heard he was losing his job two months ago, the Cisco Systems Inc. sales manager fretted about what to do next.

But in announcing the layoffs of 6,000 full-time workers like Mr. Santis, the San Jose, Calif., computer-networking company proposed an unusual option: Forgo a severance package and receive instead a third of one's salary, all benefits and stock-option awards for a year. The catch? Takers must work for that...